Fungrim entry: 42d727

\pi = \frac{5 \sqrt{\varphi + 2}}{2 \varphi} \,{}_2F_1\!\left(1, 1, \frac{3}{2}, \frac{1}{{\left(2 \varphi\right)}^{2}}\right)

TeX:

\pi = \frac{5 \sqrt{\varphi + 2}}{2 \varphi} \,{}_2F_1\!\left(1, 1, \frac{3}{2}, \frac{1}{{\left(2 \varphi\right)}^{2}}\right)

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`GoldenRatio`	$\varphi$	The golden ratio (1.618...)
`Hypergeometric2F1`	$\,{}_2F_1\!\left(a, b, c, z\right)$	Gauss hypergeometric function
`Pow`	${a}^{b}$	Power

Source code for this entry:

Entry(ID("42d727"),
    Formula(Equal(Pi, Mul(Div(Mul(5, Sqrt(Add(GoldenRatio, 2))), Mul(2, GoldenRatio)), Hypergeometric2F1(1, 1, Div(3, 2), Div(1, Pow(Mul(2, GoldenRatio), 2)))))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC